Performance of the hierarchical LMS algorithm

Woo (2001) introduced the hierarchical least mean-square (HLMS) adaptive filter algorithm, and demonstrated that it may converge faster than least mean-squares (LMS). This letter reports that the HLMS algorithm may converge to a biased impulse response, not only for colored input (as has previously been shown to be the case for the hierarchical least squares algorithm) but also for white input. We also show that, except in a special case, the penalty for faster convergence is substantially increased misadjustment noise.